Positivity Bounds without Boosts

Abstract

We derive the first positivity bounds for low-energy Effective Field Theories (EFTs) that are not invariant under Lorentz boosts. "Positivity bounds" are the low-energy manifestation of certain fundamental properties in the UV -- to date they have been used to constrain a wide variety of EFTs, however since all of the existing bounds require Lorentz invariance they are not directly applicable when this symmetry is broken, such as for most cosmological and condensed matter systems. From the UV axioms of unitarity, causality and locality, we derive an infinite family of bounds which (derivatives of) the $2\to 2$ EFT scattering amplitude must satisfy even when Lorentz boosts are broken (either spontaneously or explicitly). We apply these bounds to the leading-order EFT of both a superfluid and the scalar fluctuations produced during inflation, comparing in the latter case with the current observational constraints on primordial non-Gaussianity.

arXiv comment14 pages (including Appendices), 1 figure

References in corpus (89)

• Planck 2018 results. I. Overview and the cosmological legacy of Planck
• The Effective Field Theory of Inflation
• Causality, Analyticity and an IR Obstruction to UV Completion
• On Renormalization Group Flows in Four Dimensions
• Causality Constraints on Corrections to the Graviton Three-Point Coupling
• The Effective Field Theory of Dark Energy
• The EFT-Hedron
• Effective field theory for hydrodynamics: thermodynamics, and the derivative expansion
• The Effective Field Theory of Multifield Inflation
• Energy's and amplitudes' positivity
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• Positivity Bounds for Scalar Theories
• The Cosmological Bootstrap: Weight-Shifting Operators and Scalar Seeds
• Weak Gravity Conjecture from Unitarity and Causality
• Extremal Effective Field Theories
• Proof of the Weak Gravity Conjecture from Black Hole Entropy
• Beyond Amplitudes' Positivity and the Fate of Massive Gravity
• Softness and Amplitudes' Positivity for Spinning Particles
• Relativistic Fluids, Superfluids, Solids and Supersolids from a Coset Construction
• Amplitudes' Positivity, Weak Gravity Conjecture, and Modified Gravity
• The Cosmological Optical Theorem
• Effective Field Theory of Cosmological Perturbations
• UV complete me: Positivity Bounds for Particles with Spin
• Signs of Analyticity in Single-Field Inflation
• Infrared Consistency and the Weak Gravity Conjecture
• Consistency of the Standard Model Effective Field Theory
• On renormalization group flows and the a-theorem in 6d
• Quantum Gravity Constraints from Unitarity and Analyticity
• Building a Boostless Bootstrap for the Bispectrum
• Massive Galileon Positivity Bounds
• Positivity Bounds for Massive Spin-1 and Spin-2 Fields
• Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints
• Positivity bounds on vector boson scattering at the LHC
• Effective Lagrangian and Topological Interactions in Supersolids
• Positivity constraints on aQGC: carving out the physical parameter space
• Convex Geometry Perspective to the (Standard Model) Effective Field Theory Space
• Improved Positivity Bounds and Massive Gravity
• Positivity of Curvature-Squared Corrections in Gravity
• Positivity Bounds and the Massless Spin-2 Pole
• The Chiral Lagrangian parameters, ${\overline{\ell }}_1$, ${\overline{\ell }}_2$, are determined by the $\rho$--resonance
• Positive Signs in Massive Gravity
• Falsifying Models of New Physics Via WW Scattering
• More on gapped Goldstones at finite density: More gapped Goldstones
• QED positivity bounds
• Non-Singular Bouncing Cosmology: Consistency of the Effective Description
• On the time evolution of cosmological correlators
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Positivity in the sky
• ZZ and Zgamma still haven't found what they are looking for
• Bounds on Amplitudes in Effective Theories with Massive Spinning Particles
• Entropy Bounds on Effective Field Theory from Rotating Dyonic Black Holes
• Flavor Constraints from Unitarity and Analyticity
• Bounds on OPE Coefficients from Interference Effects in the Conformal Collider
• B-modes and the Nature of Inflation
• Spontaneous Symmetry Probing
• Massless Positivity in Graviton Exchange
• Positivity in Multi-Field EFTs
• Massive Higher Spins: Effective Theory and Consistency
• A Conformal Collider for Holographic CFTs
• Positivity Constraints on Interacting Spin-2 Fields
• Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings
• Unitary null energy condition violation in $P(X)$ cosmologies
• The Effective Theory of Shift-Symmetric Cosmologies
• Causality Constrains Higher Curvature Corrections to Gravity
• Generalized positivity bounds on chiral perturbation theory
• Wess-Zumino Terms for Relativistic Fluids, Superfluids, Solids, and Supersolids
• Causality, Unitarity and Symmetry in Effective Field Theory
• Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states
• Dynamical Constraints on RG Flows and Cosmology
• Inflation in Motion: Unitarity Constraints in Effective Field Theories with Broken Lorentz Symmetry
• Causal vs. Analytic constraints on anomalous quartic gauge couplings
• Heavy Spinning Particles from Signs of Primordial Non-Gaussianities: Beyond the Positivity Bounds
• Symmetric Superfluids
• Signs, Spin, SMEFT: Sum Rules at Dimension Six
• To Positivity and Beyond, where Higgs-Dilaton Inflation has never gone before
• UV completion without symmetry restoration
• Higher-Point Positivity
• The Cosmological Phonon: Symmetries and Amplitudes on Sub-Horizon Scales
• Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields
• Generalized elastic positivity bounds on interacting massive spin-2 theories
• Spontaneously broken boosts and the Goldstone continuum
• The Weak Gravity Conjecture, RG Flows, and Supersymmetry
• Positivity in the effective field theory of cosmological perturbations
• Boost Breaking in the EFT of Inflation
• UV Constraints on Massive Spinning Particles: Lessons from the Gravitino
• Positivity bounds on reconstructed Horndeski models
• The Cosmological Bootstrap: Inflationary Correlators from Symmetries and Singularities
• Positivity vs. Lorentz-violation: an explicit example

Cited by in corpus (17)

• Causality constraints on corrections to Einstein gravity
• Causal Effective Field Theories
• Positivity bounds on effective field theories with spontaneously broken Lorentz invariance
• Massive Gravity is not Positive
• SMEFTs living on the edge: determining the UV theories from positivity and extremality
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• Spinning Sum Rules for the Dimension-Six SMEFT
• Causality and quasi-normal modes in the GREFT
• Origin of Neutrino Masses on the Convex Cone of Positivity Bounds
• Inflationary Adler Conditions
• Bispectrum Islands
• Positivity bounds at one-loop level: the Higgs sector
• Unitarity and unstable-particle scattering amplitudes
• Perturbative unitarity bounds on field-space curvature in de Sitter spacetime: purity vs scattering amplitude
• Universal thermalization dynamics in (1+1)d QFTs
• Propagator positivity bounds for cosmological correlators
• A Tail of Eternal Inflation